PSI - Issue 41

A.E.S. Pinheiro et al. / Procedia Structural Integrity 41 (2022) 60–71 Pinheiro et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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3.2. Strength prediction This section compares the experimental results with the P m predictions for the tubular adhesive joints, considering analytical methods and the FEM, to carry out the respective validation. The analytical methods of Nayeb-Hashemi et al., and Pugno and Carpinteri, and the global yielding model (Adams et al. 1997), are analyzed. P m is obtained at the point of cohesive failure of the adhesive layer, by using continuum mechanics failure criteria, except in the CZM. The analysis is divided by adhesive types, and the adopted nomenclature is as follows: N-H for the Nayeb-Hashemi et al. model, P&C for the Pugno and Carpinteri model, GY for the global yield criterion, MPSC for the maximum peel stress criterion, MSSC for the maximum shear stress criterion, and finally MPSC+MSSC for first failure between the two criteria. All results are percentile differences between the predictions and the average P m , and defined as  P m . 3.2.1. Araldite ® AV138 Fig. 7 presents  P m between the predictions and experimental results for the AV138 for both L O =20 and 40 mm. Table 5 quantitatively shows the respective  P m .

50

0

20

30

40

 P m [%]

-50

-100

L O [mm]

N-H

P&C-MPSC P&C-MSSC

FEM-MPSC FEM-MSSC

GY

FEM-CZM

P&C-MPSC+MSSC FEM-MPSC+MSSC

Fig. 7.  P m between the predictions and experimental results for the AV138.

Table 5. Summary of  P m [%] for the AV138 and both L O . L O [mm] 20

40

N-H

-68.7 -92.8 -68.7 -92.8 24.1 -53.7 -62.1 -62.1

-72.8 -93.5 -72.8 -93.5 -59.9 -67.2 -67.2 7.5

P&C-MPSC P&C-MSSC

P&C-MPSC+MSSC

GY

FEM-MPSC FEM-MSSC

FEM-MPSC+MSSC

FEM-CZM

2.4

4.7

Data analysis for this adhesive in Fig. 7 shows that the FEM-CZM approach gives the best results, while the GY model works well for long L O but not for short L O (some joint conditions failed by adherend failure rather than the adhesive). All other methods significantly under predict the experimental P m . Table 5 shows that the analytical and FEM methods used with continuum mechanics-based failure criteria under predict the average experimental P m between 53.7% and 92.8% ( L O =20 mm), and between 59.9% and 93.5% ( L O =40 mm). The Pugno and Carpinteri, and Nayeb-Hashemi et al. models provided identical  P m for the MSSC due to the equal stress curves, as obtained in Section 3.1. Despite being strong and brittle, the AV138 manages to sustain higher loads than those predicted by first failure when the limiting stresses are attained. However, the observed deviations are transversal to the use of either the FEM or the proposed analytical models, and the FEM is validated in the literature. Thus, most of the found difference arises from the inadequacy of the failure criteria in predicting the correct joint behavior, rather than stress